Application of the Loewner-Kufarev theory to the construction of a parametric set of univalent functions of a certain form

Author:

Zadorozhnaya Olga V., ,Kochetkov Vladimir K.,

Abstract

This work relates to the theory of Loewner-Kufarev differential equations, which are a part of the geometric function theory. We apply the well-known second Loewner-Kufarev differential equation to construct a parametric family of univalent functions in the unit disk g(z, t) for each fixed non-negative value of the parameter t generalizing the known parametric families. The article also uses various alternative approaches and provides their comparative analysis. The results of the study can be considered as one sufficient condition for the uniqueness of regular functions in a unit disk. Leading Russian scientists made a great contribution to the development of the geometric function theory based the variational-parametric method for studying functionals and found some Loewner-Kufarev differential equations. There are three sections in the work. The first one applies the Loewner-Kufarev equation to construct a parametric set of univalent functions of a certain type. In the second section, we introduce a special class of regular functions in the unit disk with a fixed convex function, and prove the univalence property for functions of this class. Here we also show one more method for constructing a parametric family of univalent functions different from the methods described in the first paragraph. The third section is devoted to alternative methods for constructing one-parameter sets of univalent functions. AMS Mathematical Subject Classification: 35С15

Publisher

Tomsk State University

Subject

Mechanical Engineering,Mechanics of Materials,General Mathematics,Computational Mechanics

同舟云学术

1.学者识别学者识别

2.学术分析学术分析

3.人才评估人才评估

"同舟云学术"是以全球学者为主线,采集、加工和组织学术论文而形成的新型学术文献查询和分析系统,可以对全球学者进行文献检索和人才价值评估。用户可以通过关注某些学科领域的顶尖人物而持续追踪该领域的学科进展和研究前沿。经过近期的数据扩容,当前同舟云学术共收录了国内外主流学术期刊6万余种,收集的期刊论文及会议论文总量共计约1.5亿篇,并以每天添加12000余篇中外论文的速度递增。我们也可以为用户提供个性化、定制化的学者数据。欢迎来电咨询!咨询电话:010-8811{复制后删除}0370

www.globalauthorid.com

TOP

Copyright © 2019-2024 北京同舟云网络信息技术有限公司
京公网安备11010802033243号  京ICP备18003416号-3